Assuminga Li atom to be hydrogen-like, determinethe ionization energy of the 2s

Question

Assuminga Li atom to be hydrogen-like, determinethe ionization energy of the 2s electron. Explain qualitatively the difference from theexperimental value of 5.39 eV.
Hint: two approximations are to: a) neglect the inner electrons, orb) presume they shield the nucleus. These approximations bound thecorrect answer. Assuminga Li atom to be hydrogen-like, determinethe ionization energy of the 2s electron. Explain qualitatively the difference from theexperimental value of 5.39 eV.
Hint: two approximations are to: a) neglect the inner electrons, orb) presume they shield the nucleus. These approximations bound thecorrect answer.

Explanation / Answer

In terms of Bohr orbits the s electrons have circular orbitswhile theelectrons with l not equal to zero have elliptical orbits and thus overlap, somewhat, the l = 0orbits If you neglect the inner orbits (and adjust the nuclearaccordingly) the energy would be too large because of some shielding by eletrons in highly ellipticalorbits. If you assume complete shielding, then the energy will be toosmall because some of the inner electrons spend some of their time outside of the2s electron and the calculated energy would be too small because of the stronger nuclearattraction.

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